Abstract: For the multi-attribute clustering problem that decision information is hesitant fuzzy set (HFS) and the attribute weights are completely unknown, this paper proposes a co-correlation degree based on hesitant fuzzy cross-entropy and clustering method. In order to distinguish different HFSs, this paper defines the cross-entropy between two hesitant fuzzy elements (HFEs), and verifies the validity and rationality in comparison with the results obtained by other distance formulas. Next, this paper derives the formula of attribute weights according to the maximizing deviation algorithm from the hesitant fuzzy cross-entropy. Then, this paper proposes the concept of co-correlation degree, proves its similar properties with the traditional correlation coefficient, and considers different attributes' weight at the same time, which is determined by the formula of attribute weights. Finally, this paper uses the weighted formula of co-correlation degree for clustering analysis under hesitant fuzzy information, and verifies the feasibility and effectiveness through the comparison analysis of clustering results of diverse literature.

Key words: hesitant fuzzy set, cross-entropy, maximizing deviation, co-correlation degree, clustering analysis

摘要： 针对决策信息为犹豫模糊集且属性权重完全未知的多属性聚类问题，提出了一种基于犹豫模糊交叉熵的协相关度与聚类方法。为区分不同的犹豫模糊集，定义了犹豫模糊元的交叉熵，通过与其他距离公式得出的结果进行对比，验证了它的有效性与合理性；由犹豫模糊交叉熵公式，按照离差最大化算法得出属性权重公式；然后提出犹豫模糊集协相关度的概念，证明了它与传统相关系数类似的性质，并将协相关度公式加权；最后把加权的协相关度公式用于犹豫模糊信息下的聚类分析中，通过比较分析不同文献的聚类结果，验证了所提聚类算法的可行性与有效性。

关键词: 犹豫模糊集, 交叉熵, 离差最大化, 协相关度, 聚类分析